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There is no specification of the actual power usage of any RUT device.

Can only find voltage ranges and an "estimate" that the RUT230 can last 88 hours on a non-identified battery.
How many amps do the devices use at 12VDC?
How many watts typical, transmit, sleep, etc.?

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Sadly we have no hard-written specifications for such parameters.

Keep in mind that RUT240 has no Sleep functionality. Also, power consumption relies on specific applications. For example the more functionalities you have enabled at one given moment the more power consumption you will have.

Usually, our clients with Solar Power needs, measure one device on the field in a real situation.

Also to help improve the Watts consumed, the best option is to supply the lower voltage possible, in this case, it's 9V.
Then what was the methodology on the internal battery test of "88 hours"?
What would the maximum power usage be?

Wattage will be nearly identical regardless of voltage. Typically a 12W device will consume 1A@12V or nearly 0.89A@13.5V.if anything?

We are planning to test with the RUT240 and possibly the RUT955, when we get them at least; reseller hasn't gotten an ETA for delivery yet.

The assumption of v/A linearity is always a choice of the user depending on how much uncertainty they want in the project. The Regulator inside ar high quality but there are always diodes and other semiconductors that tend to slightly bend the power curves at different voltages.

Any ordinary Voltage/Amps datalogger would be fine to make these measurements. And if you are going to use any voltage regulator to power the unit is always safe to measure power consumption before and after the device to take into account the power loss of the conversion stage.

Also, you can take as a reference, this FCC certificate. The power consumption of the device is strictly less than 5W. In simple cases, our clients assumed 5W all the time as the worst scenario and worked all the electronics from there.